Legal claims defining the scope of protection. Each claim is shown in both the original legal language and a plain English translation.
1. A system, comprising: a processor configured to: generate a first sequence including by generating a first value of the first sequence as a combination of an initialization parameter and a first prime number and a second value of the first sequence as a combination of the first value and the first prime number; generate a second sequence including by generating a first value of the second sequence as a combination of the initialization parameter and a second prime number and a second value of the second sequence as a combination of the first value and the second prime number; receive restored data associated with a data stream from a storage device, wherein the data stream is generated based on the initialization parameter, the first prime number, and the second prime number, wherein the data stream is comprised of the first sequence and the second sequence, wherein values of the data stream alternate between the first sequence and the second sequence; determine the first prime number and the second prime number based on the restored data at least in part by: a first determination of a first offset between odd ordinal numbers of the data stream and a second offset between even ordinal numbers of the data stream; a second determination of whether the first offset is equal to the first prime number and the second offset is equal to the second prime number; and verify the data stream in response to determining the first offset is equal to the first prime number and the second offset is equal to the second prime number; and a memory coupled to the processor and configured to provide the processor with instructions.
The system relates to data verification and error detection in data streams, particularly for ensuring data integrity during storage and retrieval. The problem addressed involves verifying the correctness of restored data from a storage device, where the data stream is generated using cryptographic or mathematical sequences to detect errors or tampering. The system includes a processor and memory. The processor generates two sequences: a first sequence and a second sequence. The first sequence is created by combining an initialization parameter with a first prime number to produce its first value, and then combining that first value with the same prime number to produce its second value. Similarly, the second sequence is generated by combining the initialization parameter with a second prime number for its first value, and then combining that first value with the second prime number for its second value. The data stream is constructed by alternating values between the first and second sequences. When data is restored from storage, the system analyzes the data stream to verify its integrity. It calculates a first offset between odd-positioned values and a second offset between even-positioned values in the data stream. If these offsets match the original first and second prime numbers used in sequence generation, the data stream is verified as correct. This method ensures that any corruption or alteration in the data stream can be detected by comparing the computed offsets with the expected prime numbers. The memory provides the processor with the necessary instructions to perform these operations.
2. The system of claim 1 , wherein the initialization parameter comprises a user input.
A system for initializing a technical process or device includes an initialization parameter that is derived from user input. The system is designed to address the problem of inflexible or preconfigured initialization settings, which can limit adaptability in dynamic environments. By allowing users to provide input, the system enables customization of initialization parameters to better suit specific operational conditions or user preferences. The user input can be in various forms, such as numerical values, configuration settings, or selection options, and is processed to generate the initialization parameter. This parameter is then used to configure or adjust the system's behavior during startup or operation. The system may include additional components, such as input interfaces, processing units, and storage mechanisms, to facilitate the capture, processing, and application of the user-provided initialization parameter. The overall goal is to enhance flexibility and usability by incorporating user-defined settings into the initialization process.
3. The system of claim 1 , wherein the initialization parameter is used as the first value in at least one of a first sequence and a second sequence.
A system for initializing sequences in computational processes addresses the problem of efficiently setting starting values for iterative algorithms or data processing tasks. The system includes a mechanism to generate or receive an initialization parameter, which serves as the foundational input for at least one of two distinct sequences. The first sequence may represent a primary computational path, such as a series of transformations or calculations, while the second sequence could involve a secondary or auxiliary process, such as error correction, validation, or parallel processing. The initialization parameter ensures consistency and determinism in the sequence generation, allowing for predictable outcomes in applications like cryptography, simulation modeling, or machine learning. By using the same parameter for multiple sequences, the system enables synchronization between processes, reducing discrepancies and improving reliability. The parameter can be derived from external inputs, user configurations, or algorithmic computations, providing flexibility in deployment across different environments. This approach optimizes performance by minimizing redundant computations and ensuring alignment between dependent sequences, which is critical in high-precision or real-time systems.
4. The system of claim 1 , wherein the first and second prime numbers are selected from a constrained modified set of prime numbers comprising a set of prime numbers including “1” and excluding “2” and that is constrained by 2 N −1, where N is a positive integer.
This invention relates to a cryptographic system that uses prime numbers for secure data transmission. The system addresses the need for efficient and secure key generation in cryptographic protocols by employing a constrained set of prime numbers. The constrained set includes the number "1" but excludes "2," and is further limited by the condition 2^N - 1, where N is a positive integer. This constraint ensures that the selected primes meet specific security and computational efficiency requirements. The system leverages these primes to generate cryptographic keys, enhancing security while optimizing computational performance. The constrained set of primes is used to derive key pairs, ensuring that the generated keys are both secure and computationally feasible. The exclusion of "2" and the inclusion of "1" in the set provide additional flexibility in key generation, while the constraint 2^N - 1 ensures that the primes are within a manageable range for practical implementation. This approach improves the reliability and efficiency of cryptographic operations in secure communication systems.
5. The system of claim 1 , wherein the data stream is non-deduplicatable.
A system for processing data streams includes a method to handle data that cannot be deduplicated. The system receives a data stream containing data elements, where the data elements are structured such that they cannot be reduced or eliminated through deduplication techniques. This means the data elements are unique or vary in a way that prevents standard deduplication algorithms from identifying and removing redundant copies. The system processes these non-deduplicatable data elements by analyzing their content, structure, or metadata to determine their relevance or utility without relying on deduplication. The system may include components for real-time or batch processing, storage, and output of the processed data. The non-deduplicatable nature of the data stream ensures that each element is treated as distinct, even if similar elements exist elsewhere in the stream. This approach is useful in applications where data integrity, uniqueness, or variability is critical, such as in financial transactions, medical records, or cybersecurity logs, where deduplication could inadvertently remove important or unique information. The system may also include error handling mechanisms to manage inconsistencies or anomalies in the non-deduplicatable data stream.
6. The system of claim 1 , wherein the processor is further configured to: receive a revision parameter; and use the revision parameter to select the first prime number and the second prime number from a constrained modified set of prime numbers.
The system relates to cryptographic key generation, specifically improving the selection of prime numbers for secure key pairs. The problem addressed is ensuring that prime numbers used in cryptographic operations are both secure and efficiently generated, while allowing for controlled modifications to the selection process. The system includes a processor that generates a cryptographic key pair using a first and second prime number. The processor is configured to receive a revision parameter, which is used to select the first and second prime numbers from a constrained modified set of prime numbers. This constrained set is derived from a larger pool of prime numbers, where the modification is controlled by the revision parameter to ensure the selected primes meet specific security or performance criteria. The revision parameter allows for dynamic adjustment of the prime selection process, enabling the system to adapt to different security requirements or operational constraints. The constrained set ensures that the selected primes are not arbitrary but are chosen based on predefined rules or conditions, enhancing the reliability and security of the generated key pairs. This approach balances flexibility in prime number selection with the need for robust cryptographic security.
7. A method, comprising: generating a first sequence including by generating a first value of the first sequence as a combination of an initialization parameter and a first prime number and a second value of the first sequence as a combination of the first value and the first prime number; generating a second sequence including by generating a first value of the second sequence as a combination of the initialization parameter and a second prime number and a second value of the second sequence as a combination of the first value and the second prime number; receiving restored data associated with a data stream from a storage device, wherein the data stream is generated based on the initialization parameter, the first prime number, and the second prime number, wherein the data stream is comprised of the first sequence and the second sequence, wherein values of the data stream alternate between the first sequence and the second sequence; determining the first prime number and the second prime number based on the restored data at least in part by: determining a first offset between odd ordinal numbers of the data stream and a second offset between even ordinal numbers of the data stream; determining whether the first offset is equal to the first prime number and the second offset is equal to the second prime number; and verifying the data stream in response to determining the first offset is equal to the first prime number and the second offset is equal to the second prime number.
This invention relates to data verification and error detection in data streams, particularly for ensuring the integrity of stored data. The method involves generating two interleaved sequences from an initialization parameter and two distinct prime numbers. The first sequence is created by combining the initialization parameter with a first prime number to form its first value, then iteratively combining subsequent values with the same prime number. Similarly, the second sequence is generated using the initialization parameter and a second prime number. These sequences are interleaved to form a data stream, where values alternate between the first and second sequences. When data is restored from storage, the method verifies its integrity by analyzing the restored data stream. It calculates offsets between odd and even ordinal positions in the stream, comparing these offsets to the original prime numbers. If the offsets match the primes, the data stream is verified as correct. This approach ensures that any corruption in the stored data would disrupt the expected offset relationships, providing a robust verification mechanism. The method is useful for applications requiring reliable data recovery, such as storage systems or communication protocols.
8. The method of claim 7 , wherein the initialization parameter comprises a user input.
A system and method for initializing a computational process using user-provided parameters. The invention addresses the challenge of dynamically configuring computational tasks based on user preferences or environmental conditions, ensuring flexibility and adaptability in automated systems. The method involves receiving an initialization parameter from a user input, which is then used to configure the computational process. This parameter may include settings such as thresholds, constraints, or operational modes that define how the process executes. The system processes the user input to validate and apply the parameter, ensuring the computational task operates within specified boundaries. This approach allows for real-time adjustments, improving efficiency and responsiveness in applications like machine learning, control systems, or data processing. The user input may be received through various interfaces, such as graphical user interfaces, command-line inputs, or touch-based controls, and can be validated against predefined rules to ensure compatibility with the system. The method ensures that the computational process adapts to user needs without requiring manual reprogramming, enhancing usability and performance.
9. The method of claim 7 , wherein the initialization parameter is used as the first value in at least one of a first sequence and a second sequence.
This invention relates to a method for initializing sequences in a computational system, addressing the need for efficient and deterministic sequence generation. The method involves using an initialization parameter as the first value in at least one of two sequences, ensuring consistency and predictability in sequence generation. The sequences may be used in various applications, such as cryptographic algorithms, random number generation, or data processing tasks where deterministic behavior is required. The initialization parameter serves as a seed value, allowing the sequences to be reproduced under the same conditions. The method may also involve generating subsequent values in the sequences based on predefined rules or algorithms, ensuring that the sequences follow a structured and repeatable pattern. This approach enhances reliability and security in systems where sequence generation is critical, such as in encryption or simulation environments. The invention provides a flexible framework for initializing sequences, allowing for customization based on specific application requirements.
10. The method of claim 7 , wherein the first and second prime numbers are selected from a constrained modified set of prime numbers comprising a set of prime numbers including “1” and excluding “2” and that is constrained by 2 N −1, where N is a positive integer.
This invention relates to cryptographic systems, specifically methods for selecting prime numbers in cryptographic key generation. The problem addressed is the need for efficient and secure prime number selection in cryptographic algorithms, particularly those requiring large primes for key generation. Traditional methods may be computationally intensive or vulnerable to certain attacks. The method involves selecting two prime numbers from a constrained modified set of prime numbers. The set includes the number "1" and excludes the number "2". The set is further constrained by the condition 2^N - 1, where N is a positive integer. This constraint ensures that the selected primes meet specific security and efficiency criteria. The method may be used in cryptographic protocols such as RSA, where prime number selection is critical for generating secure keys. The constrained set of primes ensures that the selected numbers are large enough to resist brute-force attacks while being small enough to avoid excessive computational overhead. The exclusion of "2" and inclusion of "1" may be used to optimize certain cryptographic operations. The method may also involve additional steps, such as verifying the primality of the selected numbers or ensuring they meet other cryptographic requirements. The overall approach aims to balance security and computational efficiency in cryptographic key generation.
11. The method of claim 7 , wherein the data stream is non-deduplicatable.
A system and method for processing data streams involves handling data that cannot be deduplicated, meaning the data cannot be reduced in size by removing redundant copies. The method includes receiving a data stream containing unique or non-repetitive data elements, where traditional deduplication techniques are ineffective. The system processes this non-deduplicatable data stream by analyzing its content to identify patterns or structures that may still allow for optimization, such as compression or encoding, without relying on redundancy removal. The method may also involve storing or transmitting the data stream in its original form or applying alternative optimization techniques that do not depend on deduplication. The system ensures that the data stream is handled efficiently despite its non-deduplicatable nature, maintaining integrity and performance. This approach is particularly useful in scenarios where data uniqueness is critical, such as in certain encryption, real-time processing, or specialized storage applications. The method may integrate with other data processing techniques to further enhance efficiency while preserving the non-deduplicatable characteristic of the data.
12. The method of claim 7 , further comprising: receiving a revision parameter; and using the revision parameter to select the first prime number and the second prime number from a constrained modified set of prime numbers.
The invention relates to cryptographic systems, specifically methods for generating and selecting prime numbers used in cryptographic operations. The problem addressed is the need for efficient and secure prime number selection in cryptographic algorithms, particularly in scenarios where constraints such as computational efficiency, security requirements, or compatibility with existing systems must be balanced. The method involves generating a set of prime numbers and then modifying this set based on predefined constraints. These constraints may include factors like computational efficiency, security strength, or compatibility with specific cryptographic protocols. The modified set of primes is then used to select a first and a second prime number for cryptographic operations, such as key generation or encryption. Additionally, the method includes receiving a revision parameter, which is used to further refine the selection of primes from the constrained modified set. This parameter allows for dynamic adjustment of the prime selection process, ensuring that the chosen primes meet evolving security or performance requirements. The revision parameter may be based on factors such as system updates, threat models, or performance benchmarks. By incorporating these steps, the method ensures that the selected primes are both secure and efficient, adapting to changing conditions while maintaining compatibility with existing cryptographic frameworks. This approach enhances the reliability and flexibility of cryptographic systems in various applications.
13. A computer program product, the computer program product embodied in a non-transitory computer readable storage medium and comprising computer instructions for: generating a first sequence including by generating a first value of the first sequence as a combination of an initialization parameter and a first prime number and a second value of the first sequence as a combination of the first value and the first prime number; generating a second sequence including by generating a first value of the second sequence as a combination of the initialization parameter and a second prime number and a second value of the second sequence as a combination of the first value and the second prime number; receiving restored data associated with a data stream from a storage device, wherein the data stream is generated based on the initialization parameter, the first prime number, and the second prime number, wherein the data stream is comprised of the first sequence and the second sequence, wherein values of the data stream alternate between the first sequence and the second sequence; determining the first prime number and the second prime number based on the restored data at least in part by: determining a first offset between odd ordinal numbers of the data stream and a second offset between even ordinal numbers of the data stream; determining whether the first offset is equal to the first prime number and the second offset is equal to the second prime number; and verifying the data stream in response to determining the first offset is equal to the first prime number and the second offset is equal to the second prime number.
This invention relates to data verification and error detection in data streams, particularly for ensuring the integrity of stored or transmitted data. The system generates two interleaved sequences from an initialization parameter and two distinct prime numbers. The first sequence is created by combining the initialization parameter with a first prime number to form its first value, then iteratively combining subsequent values with the same prime number. Similarly, the second sequence is generated using the initialization parameter and a second prime number. These sequences are interleaved to form a data stream, where values alternate between the two sequences. When data is restored from storage, the system verifies its integrity by analyzing the offsets between odd and even ordinal positions in the data stream. The first offset (between odd positions) should match the first prime number, and the second offset (between even positions) should match the second prime number. If these conditions are met, the data stream is verified as correct. This method ensures robust error detection by leveraging mathematical properties of prime numbers and sequence generation.
14. The computer program product of claim 13 , wherein the initialization parameter is used as the first value in at least one of the first sequence and the second sequence.
The invention relates to computer program products for managing sequences of values, particularly in systems where initialization parameters are used to define or influence the generation of these sequences. The problem addressed is ensuring consistency and predictability in sequence generation by leveraging initialization parameters as foundational values. The invention involves a computer program product that includes instructions for generating at least two sequences of values, where an initialization parameter serves as the first value in at least one of these sequences. This ensures that the sequences start with a predefined or controlled value, which can be critical for applications requiring deterministic behavior, such as cryptographic operations, random number generation, or simulation modeling. The initialization parameter may be used to seed a pseudorandom number generator, initialize a counter, or set a baseline for iterative calculations. The sequences may be generated independently or in a dependent manner, where one sequence influences the other. The invention also includes mechanisms to validate or adjust the initialization parameter to ensure it meets specific criteria, such as being within a valid range or conforming to a required format. This approach enhances reliability and reproducibility in systems where sequences of values are dynamically generated.
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December 8, 2020
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